Geodesic
Existence and multiplicity of solutions for sublinear ordinary differential equations at resonance
Electronic journal of differential equations, Tome 2015 (2015)
Using a

$ \mathcal{L} u(t)=\mu u(t)+W_u(t,u(t)),\quad 0\leq t\leq L $

with suitable periodic or boundary conditions. Here $\mathcal{L}$ is a linear positive selfadjoint operator, $\mu$ is a parameter between two egienvalues of this operator, and $W_u$ is the gradient of a potential function.
Classification : 58E05, 34C37, 70H05
Keywords: sublinear potential, $Z_2$ type index theorem, critical point, resonance, Hamiltonian system 
@article{EJDE_2015__2015__a61,
     author = {Li,  Chengyue and Chen,  Fenfen},
     title = {Existence and multiplicity of solutions for sublinear ordinary differential equations at resonance},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1327.34070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a61/}
}
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%A Chen,  Fenfen
%T Existence and multiplicity of solutions for sublinear ordinary differential equations at resonance
%J Electronic journal of differential equations
%D 2015
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%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a61/
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Li,  Chengyue; Chen,  Fenfen. Existence and multiplicity of solutions for sublinear ordinary differential equations at resonance. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a61/